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M K.

asked • 11/11/13

Operations of Functions! (Division) And some other stuff...

How would you solve this f(x)⁄g(x) problem (please include ALL steps and an explanation for each)?
 
f(x)=(5x+11)/(x2-9)
g(x)= (4x-2)/(x2-9)
 
 
Also, would the domain end up being (-∞, -3) U (-3, 1/2) U (1/2, 3) U (3, ∞)? Or would there be no 1/2? From what I think I got, the denominator should be 2(2x-1), so the denominator couldn't be 0, so it can't be 1/2. Am I right? Or would we just be looking in the middle of the solving/simplifying?
 
One last thing: when do we look in problems like these to get our domain (like when do we look to see what values are not included)? 
 
Thanks!

2 Answers By Expert Tutors

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Nataliya D. answered • 11/11/13

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Vivian L.

I understand your point.
However, in algebra, the priorities are...
SIMPLIFY
FACTOR
EVALUATE
SOLVE
Evaluation of domain does not come before simplification.
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11/11/13

Nataliya D.

In any branch of mathematics the first priority is to identify the critical points in order to avoid any mistake.
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11/11/13

Vivian L.

Then the algebraic processes should be...
EVALUATE
SIMPLIFY
FACTOR
SOLVE
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11/11/13

M K.

I found out that Nataliya was right; we find any values that do not fit the domain throughout, so the 1/2 would be correct in the domain. So I guess we'd have to go through the WHOLE process and catch any critical numbers, or numbers that don't fit the domain. Is that correct?
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11/12/13

Vivian L.

Thank you for the update.
It is correct, if, as I explain above, the algebraic processes are deemed incorrect.
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11/13/13

Vivian L. answered • 11/11/13

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Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH

M K.

Yes, this matches up with what I got! Thanks! I'll make sure to ask while reviewing for our test.
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11/11/13

Vivian L.

Please tell me the answer the instructor provides because I also need to know.
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11/11/13

M K.

Okay, I will respond as soon as I find out!
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11/11/13

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